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(a) Assuming true randomness what is the probability that you picked the fair coin (event C,)? (b) Suppose that the coin came up heads (event H1). What is the posterior probability that you picked the fair coin? (c) Now suppose that you toss the same coin again. What is the probability that the coin comes up heads on the second toss (event Hz)?

(a) Assuming true randomness what is the probability that you picked the fair coin (event C,)? (b) Suppose that the coin came up heads (event H1). What is the posterior probability that you picked the fair coin? (c) Now suppose that you toss the same coin again. What is the probability that the coin comes up heads on the second toss (event Hz)?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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M-7 Please I need help with this question needed very clearly and step by step explanation and needed with clear handwriting please, will be really appreciated for your help

ONLY NEEDED PARTS A,B AND C ONLY

7. Depending on the sample space, some events might not be independent, but they are conditionally independent, meaning that they become independent after conditioning on some third event. You have a box with two coins: one of them is fair, the other has two heads. You pick a coin at random and toss it. Let C be the event that you picked the fair coin, and let C2 be the event that you picked the two-headed coin. (a) Assuming true randomness what is the probability that you picked the fair coin (event C,)? (b) Suppose that the coin came up heads (event H). What is the posterior probability that you picked the fair coin? (c) Now suppose that you toss the same coin again. What is the probability that the coin comes up heads on the second toss (event H2)? (d) What is the probability that the coin comes up heads twice (event Hin H2)? (It may be helpful to draw a tree diagram.) Compare this to the product P (Hi)P (H2) and conclude that the two events H1 and H2 are not independent. (e) Calculate the probabilities P (H1 n Hz Ci) and compare with the products P(H1 | C)P(H2 | C) to conclude that the events H, and Hz are conditionally independent after we know which coin we picked. (f) Compute the posterior probability that you picked the fair coin given that both tosses came up heads?
Transcribed Image Text:7. Depending on the sample space, some events might not be independent, but they are conditionally independent, meaning that they become independent after conditioning on some third event. You have a box with two coins: one of them is fair, the other has two heads. You pick a coin at random and toss it. Let C be the event that you picked the fair coin, and let C2 be the event that you picked the two-headed coin. (a) Assuming true randomness what is the probability that you picked the fair coin (event C,)? (b) Suppose that the coin came up heads (event H). What is the posterior probability that you picked the fair coin? (c) Now suppose that you toss the same coin again. What is the probability that the coin comes up heads on the second toss (event H2)? (d) What is the probability that the coin comes up heads twice (event Hin H2)? (It may be helpful to draw a tree diagram.) Compare this to the product P (Hi)P (H2) and conclude that the two events H1 and H2 are not independent. (e) Calculate the probabilities P (H1 n Hz Ci) and compare with the products P(H1 | C)P(H2 | C) to conclude that the events H, and Hz are conditionally independent after we know which coin we picked. (f) Compute the posterior probability that you picked the fair coin given that both tosses came up heads?
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